Focusing of shifted vortex beams of arbitrary order with different polarization

Pictures of focused shifted vortex beams, regardless of the order of the vortex and displacement, look approximately the same, as a crescent. To obtain another type of focal pictures, an optical vortex of the opposite sign can be used as an illuminating beam. For the numerical study of the considered effects simultaneously at several optical vortices of different orders, directions of rotation and polarization, a multi-order diffraction optical element was used in the conditions of sharp focusing. It is shown, that named characteristics significantly change the form of rotating intensity in the focal area. It may be useful for optical manipulations.